{ "cells": [ { "cell_type": "markdown", "id": "f53f2418", "metadata": {}, "source": [ "# Bracketing Method\n", "**강좌**: *수치해석*" ] }, { "cell_type": "markdown", "id": "83e2f29d", "metadata": {}, "source": [ "## 그래프를 이용한 방정식 해 찾기\n", "[낙하산병 문제](../contents/Lecture_01_Exercise_101.ipynb) 에서 아래를 상황을 생각해보자.\n", "\n", "질량 $m=68.1kg$인 낙하산병이 자유낙하할 때 10초 후 속도가 $40m/s$ 가 되는 항력 계수는 얼마인가?\n", "\n", "엄밀해를 이용하면 다음과 같다.\n", "\n", "$$\n", "f(c)= \\frac{mg}{c} (1 - e^{(-c/m)t}) - 40 = \\frac{9.81(68.1)}{c} (1 - e^{(-c/68.1)10})\n", "$$" ] }, { "cell_type": "code", "execution_count": 1, "id": "061afab9", "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "from matplotlib import pyplot as plt\n", "\n", "import numpy as np\n", "\n", "plt.style.use('ggplot')\n", "plt.rcParams['figure.dpi'] = 150" ] }, { "cell_type": "code", "execution_count": 2, "id": "66039494", "metadata": {}, "outputs": [], "source": [ "# 주요 상수\n", "m = 68.1\n", "g = 9.81\n", "t = 10\n", "\n", "\n", "def f(c):\n", " # using the exact solution\n", " return m*g/c*(1 - np.exp(-c/m*t)) - 40" ] }, { "cell_type": "code", "execution_count": 3, "id": "e5d42094", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4 34.19047156669296\n", "8 17.712257537470236\n", "12 6.113943075921462\n", "16 -2.230260706051183\n", "20 -8.368384465361824\n" ] } ], "source": [ "# 4~20 사이에서 값 계산\n", "for c in range(4, 21, 4):\n", " print(c, f(c))" ] }, { "cell_type": "code", "execution_count": 4, "id": "11a1a0e8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 초기 Guess (0, 20)\n", "c = np.linspace(1, 20, 101)\n", "\n", "# Plot\n", "plt.plot(c, f(c))\n", "\n", "# From graph\n", "plt.plot(14.75, f(14.85), marker='x')\n", "\n", "plt.xlabel('x')\n", "plt.ylabel('y')" ] }, { "cell_type": "markdown", "id": "647f1287", "metadata": {}, "source": [ "## Bisection Method\n", "그래프로 구하는 과정을 체계적으로 생각해보면, 구간을 정하고 양 끝 점에서 부호가 같은지 다른지 확인하고 구간을 줄여 나간다.\n", "\n", "$$\n", "f(a)\\times f(b) < 0\n", "$$\n", "\n", "### 알고리즘\n", "* 해가 구간 (a, b) 사이에 있을 때 해가 존재하면 $f(a)\\cdot f(b) < 0$ 조건을 활용한다.\n", "\n", "* 이 경우 중간 값 $c=\\frac{a+b}{2}$ 에 대해 \n", "\n", " * $f(a)\\cdot f(c) < 0$ 이면 해가 (a, c) 사이에 있다고 범위를 좁힘\n", " \n", " * $f(c)\\cdot f(b) < 0$ 이면 해가 (c, b) 사이에 있다고 범위를 좁힘\n", "\n", ":::{figure-md} markdown-fig\n", "\"bisect-fig\"\n", "\n", "Bisection method (From Wikipedia)\n", ":::" ] }, { "cell_type": "markdown", "id": "463ea597", "metadata": {}, "source": [ "### By hand\n", "첫번째 구간을 [12, 16] 으로 한 후 진행해보자" ] }, { "cell_type": "code", "execution_count": 5, "id": "aa45d3e9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.True_" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a, b = 12, 16\n", "\n", "# Check if the solution lies within the interval [a, b]\n", "f(a)*f(b) < 0" ] }, { "cell_type": "code", "execution_count": 6, "id": "f50bac58", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(np.False_, np.True_)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Midpoint\n", "c = 0.5*(a + b)\n", "\n", "# 해가 [a, c]. [c, b] 중 어디에 존재하는지 확인\n", "f(a)*f(c) < 0, f(c)*f(b) < 0" ] }, { "cell_type": "code", "execution_count": 7, "id": "77550ae6", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "New interval: (14.0, 16)\n" ] } ], "source": [ "# 범위를 좁힘\n", "a = c\n", "print(\"New interval: {}\".format((a, b)))" ] }, { "cell_type": "code", "execution_count": 8, "id": "638c9b78", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(np.True_, np.False_)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Midpoint\n", "c = 0.5*(a + b)\n", "\n", "# 해가 [a, c]. [c, b] 중 어디에 존재하는지 확인\n", "f(a)*f(c) < 0, f(c)*f(b) < 0" ] }, { "cell_type": "code", "execution_count": 9, "id": "b4f4aaae", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "New interval: (14.0, 15.0)\n" ] } ], "source": [ "# 범위를 좁힘\n", "b = c\n", "print(\"New interval: {}\".format((a, b)))" ] }, { "cell_type": "code", "execution_count": 10, "id": "9cf48ef3", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(np.False_, np.True_)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Midpoint\n", "c = 0.5*(a + b)\n", "\n", "# 해가 [a, c]. [c, b] 중 어디에 존재하는지 확인\n", "f(a)*f(c) < 0, f(c)*f(b) < 0" ] }, { "cell_type": "code", "execution_count": 11, "id": "1131eedf", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "New interval: (14.5, 15.0)\n" ] } ], "source": [ "# 범위를 좁힘\n", "a = c\n", "print(\"New interval: {}\".format((a, b)))" ] }, { "cell_type": "code", "execution_count": 12, "id": "81915125", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(np.False_, np.True_)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Midpoint\n", "c = 0.5*(a + b)\n", "\n", "# 해가 [a, c]. [c, b] 중 어디에 존재하는지 확인\n", "f(a)*f(c) < 0, f(c)*f(b) < 0" ] }, { "cell_type": "code", "execution_count": 13, "id": "e86ed401", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "New interval: (14.75, 15.0)\n" ] } ], "source": [ "# 범위를 좁힘\n", "a = c\n", "print(\"New interval: {}\".format((a, b)))" ] }, { "cell_type": "code", "execution_count": 14, "id": "9a4cd2a5", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(np.True_, np.False_)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Midpoint\n", "c = 0.5*(a + b)\n", "\n", "# 해가 [a, c]. [c, b] 중 어디에 존재하는지 확인\n", "f(a)*f(c) < 0, f(c)*f(b) < 0" ] }, { "cell_type": "code", "execution_count": 15, "id": "2bb36b7e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "New interval: (14.75, 14.875)\n" ] } ], "source": [ "# 범위를 좁힘\n", "b = c\n", "print(\"New interval: {}\".format((a, b)))" ] }, { "cell_type": "code", "execution_count": 16, "id": "ac49f4b0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(np.True_, np.False_)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Midpoint\n", "c = 0.5*(a + b)\n", "\n", "# 해가 [a, c]. [c, b] 중 어디에 존재하는지 확인\n", "f(a)*f(c) < 0, f(c)*f(b) < 0" ] }, { "cell_type": "code", "execution_count": 17, "id": "c7ec330c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "New interval: (14.75, 14.8125)\n" ] } ], "source": [ "# 범위를 좁힘\n", "b = c\n", "print(\"New interval: {}\".format((a, b)))" ] }, { "cell_type": "code", "execution_count": 18, "id": "4621bc85", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(np.False_, np.True_)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Midpoint\n", "c = 0.5*(a + b)\n", "\n", "# 해가 [a, c]. [c, b] 중 어디에 존재하는지 확인\n", "f(a)*f(c) < 0, f(c)*f(b) < 0" ] }, { "cell_type": "code", "execution_count": 19, "id": "f26a0e49", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "New interval: (14.78125, 14.8125)\n" ] } ], "source": [ "# 범위를 좁힘\n", "a = c\n", "print(\"New interval: {}\".format((a, b)))" ] }, { "cell_type": "code", "execution_count": 20, "id": "ca38a6ec", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(np.False_, np.True_)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Midpoint\n", "c = 0.5*(a + b)\n", "\n", "# 해가 [a, c]. [c, b] 중 어디에 존재하는지 확인\n", "f(a)*f(c) < 0, f(c)*f(b) < 0" ] }, { "cell_type": "markdown", "id": "8a5d0d13", "metadata": {}, "source": [ "#### 종료 판정 기준\n", "위 과정은 무한히 계속될 수 있다. 적당한 해상도 이내에서 계산이 되었으면 멈춰야 한다.\n", "\n", "즉 오차가 일정 수준 이내, 상대 오차가 일정 수준 이내이면 멈추기로 한다.\n", "\n", "엄밀해를 모르므로 근사 상대 오차 $\\epsilon_a$ 의 크기가 $tol$ 보다 작으면 멈춘다.\n", "\n", " \n", ":::{note}\n", "$\\epsilon_a< tol$ 이면 멈춘다.\n", ":::" ] }, { "cell_type": "markdown", "id": "fc5a6617", "metadata": {}, "source": [ "### Make a code\n", "`if` 구문으로 어떤 쪽으로 선택할 지 만들어 본다." ] }, { "cell_type": "code", "execution_count": 21, "id": "e94ff849", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 14.0 16 15.0\n", "1 14.0 15.0 14.5\n", "2 14.5 15.0 14.75\n", "3 14.75 15.0 14.875\n", "4 14.75 14.875 14.8125\n", "5 14.75 14.8125 14.78125\n", "6 14.78125 14.8125 14.796875\n", "7 14.796875 14.8125 14.8046875\n", "8 14.796875 14.8046875 14.80078125\n", "9 14.80078125 14.8046875 14.802734375\n", "10 14.80078125 14.802734375 14.8017578125\n", "11 14.80078125 14.8017578125 14.80126953125\n", "12 14.80078125 14.80126953125 14.801025390625\n", "13 14.801025390625 14.80126953125 14.8011474609375\n", "14 14.801025390625 14.8011474609375 14.80108642578125\n", "15 14.80108642578125 14.8011474609375 14.801116943359375\n", "16 14.801116943359375 14.8011474609375 14.801132202148438\n", "Converged at 14.801139831542969\n" ] } ], "source": [ "a, b = 12, 16\n", "c = 0.5*(a+b)\n", "\n", "iter_max = 20\n", "for i in range(iter_max):\n", " if f(a)*f(c) < 0:\n", " b = c\n", " elif f(b)*f(c) < 0:\n", " a = c\n", "\n", " # Save old midpoint\n", " c0 = c\n", " \n", " # Compute new midpoint\n", " c = 0.5*(a + b)\n", " \n", " # Compute relative error\n", " if abs((c0 - c)/c) < 1e-6:\n", " # Stop and write converged solution\n", " print(\"Converged at {}\".format(c))\n", " break\n", " else:\n", " print(i, a, b, c)" ] }, { "cell_type": "markdown", "id": "406c917c", "metadata": {}, "source": [ "엄밀해가 $c = 14.8011$ 임을 이용해서 상대오차를 구해보자." ] }, { "cell_type": "code", "execution_count": 22, "id": "89db4bee", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 14.0 16 15.0 0.013438190404767219 0.06666666666666667\n", "1 14.0 15.0 14.5 0.020343082608725024 0.034482758620689655\n", "2 14.5 15.0 14.75 0.003452446101978902 0.01694915254237288\n", "3 14.75 15.0 14.875 0.004992872151394158 0.008403361344537815\n", "4 14.75 14.875 14.8125 0.0007702130247076283 0.004219409282700422\n", "5 14.75 14.8125 14.78125 0.0013411165386356368 0.0021141649048625794\n", "6 14.78125 14.8125 14.796875 0.00028545175696400427 0.0010559662090813093\n", "7 14.796875 14.8125 14.8046875 0.00024238063387181202 0.0005277044854881266\n", "8 14.796875 14.8046875 14.80078125 2.1535561546096118e-05 0.0002639218791237794\n", "9 14.80078125 14.8046875 14.802734375 0.00011042253616285795 0.00013194352816994325\n", "10 14.80078125 14.802734375 14.8017578125 4.444348730838091e-05 6.597611664577422e-05\n", "11 14.80078125 14.8017578125 14.80126953125 1.1453962881142397e-05 3.298914657077821e-05\n", "12 14.80078125 14.80126953125 14.801025390625 5.040799332476861e-06 1.6494845360824743e-05\n", "13 14.801025390625 14.80126953125 14.8011474609375 3.2065817743327684e-06 8.247354660992487e-06\n", "14 14.801025390625 14.8011474609375 14.80108642578125 9.171087790720461e-07 4.123694335281092e-06\n", "15 14.80108642578125 14.8011474609375 14.801116943359375 1.1447364976303612e-06 2.0618429164355686e-06\n", "16 14.801116943359375 14.8011474609375 14.801132202148438 2.175659135981565e-06 1.030920395419827e-06\n", "Converged at 14.801139831542969\n" ] } ], "source": [ "a, b = 12, 16\n", "c = 0.5*(a+b)\n", "\n", "c_ex = 14.8011\n", "\n", "# 상대오차 (참, 근사)\n", "eps_t = []\n", "eps_a = []\n", "\n", "iter_max = 20\n", "for i in range(iter_max):\n", " if f(a)*f(c) < 0:\n", " b = c\n", " elif f(b)*f(c) < 0:\n", " a = c\n", "\n", " # Save old midpoint\n", " c0 = c\n", " \n", " # Compute new midpoint\n", " c = 0.5*(a + b)\n", " \n", " # Compute relative error\n", " eps_ti = abs((c - c_ex)/c_ex)\n", " eps_ai = abs((c0 - c)/c)\n", " eps_t.append(eps_ti)\n", " eps_a.append(eps_ai)\n", " \n", " if eps_ai < 1e-6:\n", " # Stop and write converged solution\n", " print(\"Converged at {}\".format(c))\n", " break\n", " else:\n", " print(i, a, b, c, eps_ti, eps_ai)" ] }, { "cell_type": "code", "execution_count": 23, "id": "7b54a9e4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Error')" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.semilogy(eps_t)\n", "plt.semilogy(eps_a)\n", "\n", "plt.legend(['True', 'Approximation'])\n", "plt.xlabel('Iter')\n", "plt.ylabel('Error')" ] }, { "cell_type": "markdown", "id": "f6815cab", "metadata": {}, "source": [ "- Bisection method를 진행하면서 오차의 범위가 절반씩 줄어든다." ] }, { "cell_type": "markdown", "id": "19fa81cb", "metadata": {}, "source": [ "#### Recursive algorithm\n", "\n", "함수 안에서 함수를 호출\n", "\n", ":::{figure-md} Recursive-algorihm\n", "\"recursiv-fig\"\n", "\n", "Recursive algorihm (From Wikipedia)\n", ":::\n", "\n", ":::{note}\n", "$\\epsilon_a$ 계산시 $c=0$ 일 때 분모가 0이 될 수 있다. 분모에 매우 작은 값을 더하자.\n", ":::" ] }, { "cell_type": "code", "execution_count": 24, "id": "861d1cf0", "metadata": {}, "outputs": [], "source": [ "def bisect(a, b, f, c0=a, tol=1e-6):\n", " \"\"\"\n", " Bisection method\n", " \n", " Parameters\n", " ----------\n", " a : float\n", " Lower limit\n", " b : float\n", " Upper limit\n", " c0 : float\n", " Previous solution\n", " f : function\n", " 함수\n", " tol : float\n", " Tolerance\n", " \"\"\"\n", " fa, fb = f(a), f(b)\n", " product = fa*fb\n", "\n", " # 구간 경계에서 해가 존재한 경우\n", " if product == 0:\n", " if fa == 0:\n", " print('Converged at {:.7g}'.format(a))\n", " \n", " return a\n", " else:\n", " print('Converged at {:.7g}'.format(b)) \n", " \n", " return b\n", " \n", " elif product > 0:\n", " # 같은 부호 이므로 이 구간 내에 해가 존재하지 않음\n", " raise ValueError('Wrong Intervals')\n", " \n", " else:\n", " c = 0.5*(a+b)\n", " \n", " # Convergence 조건\n", " if (abs(c - c0)/ max(abs(c), tol)) < tol:\n", " print('Converged at {:.7g}'.format(c))\n", " \n", " return c\n", " elif fa*f(c) < 0:\n", " # 해는 (a,c) 사이에 존재함, 범위 좁히기\n", " bisect(a, c, f, c, tol)\n", " else:\n", " # 해는 (c,a) 사이에 존재함, 범위 좁히기\n", " bisect(c, b, f, c, tol)" ] }, { "cell_type": "code", "execution_count": 25, "id": "4f0341c0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Converged at 14.80114\n" ] } ], "source": [ "bisect(12, 16, f)" ] }, { "cell_type": "markdown", "id": "3041e8f2", "metadata": {}, "source": [ "### 구간 설정\n", "- Bracketing method는 적절한 구간 설정이 중요함\n", "- 1개의 해를 포함하는 구간을 설정해야 함" ] }, { "cell_type": "code", "execution_count": 26, "id": "2ab1eeb5", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.arange(-10, 10, 0.1)\n", "\n", "def f1(x):\n", " return x**2 + 10*np.sin(x)\n", "\n", "plt.plot(x, f1(x))\n", "plt.xlabel('x')\n", "plt.ylabel('y')\n", "plt.legend([r\"$x^2 + 10\\sin(x)$\"])" ] }, { "cell_type": "code", "execution_count": 27, "id": "d582c2e7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Converged at -2.479483\n" ] } ], "source": [ "# Left solution\n", "bisect(-10, -1, f1)" ] }, { "cell_type": "code", "execution_count": 28, "id": "b6b4140e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(0.0)" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f1(0)" ] }, { "cell_type": "code", "execution_count": 29, "id": "6e5b1a93", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Converged at 0\n" ] } ], "source": [ "# Right solution\n", "bisect(-1, 1, f1)" ] }, { "cell_type": "code", "execution_count": 30, "id": "bf9e4b46", "metadata": {}, "outputs": [ { "ename": "ValueError", "evalue": "Wrong Intervals", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", "Cell \u001b[0;32mIn[30], line 2\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[38;5;66;03m# Wrong Interval 1\u001b[39;00m\n\u001b[0;32m----> 2\u001b[0m \u001b[43mbisect\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[38;5;241;43m10\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[38;5;241;43m5\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mf1\u001b[49m\u001b[43m)\u001b[49m\n", "Cell \u001b[0;32mIn[24], line 34\u001b[0m, in \u001b[0;36mbisect\u001b[0;34m(a, b, f, c0, tol)\u001b[0m\n\u001b[1;32m 30\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m b\n\u001b[1;32m 32\u001b[0m \u001b[38;5;28;01melif\u001b[39;00m product \u001b[38;5;241m>\u001b[39m \u001b[38;5;241m0\u001b[39m:\n\u001b[1;32m 33\u001b[0m \u001b[38;5;66;03m# 같은 부호 이므로 이 구간 내에 해가 존재하지 않음\u001b[39;00m\n\u001b[0;32m---> 34\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mWrong Intervals\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m 36\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 37\u001b[0m c \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0.5\u001b[39m\u001b[38;5;241m*\u001b[39m(a\u001b[38;5;241m+\u001b[39mb)\n", "\u001b[0;31mValueError\u001b[0m: Wrong Intervals" ] } ], "source": [ "# Wrong Interval 1\n", "bisect(-10, -5, f1)" ] }, { "cell_type": "code", "execution_count": 31, "id": "cf758380", "metadata": {}, "outputs": [ { "ename": "ValueError", "evalue": "Wrong Intervals", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", "Cell \u001b[0;32mIn[31], line 2\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[38;5;66;03m# Wrong Interval 2\u001b[39;00m\n\u001b[0;32m----> 2\u001b[0m \u001b[43mbisect\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[38;5;241;43m5\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m5\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mf1\u001b[49m\u001b[43m)\u001b[49m\n", "Cell \u001b[0;32mIn[24], line 34\u001b[0m, in \u001b[0;36mbisect\u001b[0;34m(a, b, f, c0, tol)\u001b[0m\n\u001b[1;32m 30\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m b\n\u001b[1;32m 32\u001b[0m \u001b[38;5;28;01melif\u001b[39;00m product \u001b[38;5;241m>\u001b[39m \u001b[38;5;241m0\u001b[39m:\n\u001b[1;32m 33\u001b[0m \u001b[38;5;66;03m# 같은 부호 이므로 이 구간 내에 해가 존재하지 않음\u001b[39;00m\n\u001b[0;32m---> 34\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mWrong Intervals\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m 36\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 37\u001b[0m c \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0.5\u001b[39m\u001b[38;5;241m*\u001b[39m(a\u001b[38;5;241m+\u001b[39mb)\n", "\u001b[0;31mValueError\u001b[0m: Wrong Intervals" ] } ], "source": [ "# Wrong Interval 2\n", "bisect(-5, 5, f1)" ] }, { "cell_type": "markdown", "id": "daab9bc2", "metadata": {}, "source": [ "### DIY\n", "`For-Loop` 를 이용하여 Bisection method 계산 함수를 만드시오. 아래 기능도 같이 구현하시오.\n", "- boolean 형식의 *verbose* keyword argument를 추가하라.\n", " * True 일 경우 중간 계산 결과 및 상대 오차를 출력한다.\n", " * False 일 경우 최종 해만 출력한다.\n", " * 기본 값은 False로 한다." ] }, { "cell_type": "markdown", "id": "3ec61587", "metadata": {}, "source": [ "## Method of False Position\n", "\n", "Bisection method 보다 계산 효율을 높이기 위해 가 위치 (False position)를 사용한다.\n", "\n", "이 위치는 중점 대신에 양 끝점을 직선으로 이었을 때 교점을 사용한다.\n", "\n", "아래 그림을 보면 다음 관계로 가 위치를 구한다.\n", "\n", "$$\n", "\\frac{f(a)}{c - a} = \\frac{f(b)}{c - b}\n", "$$\n", "\n", "이를 정리하면 다음과 같다.\n", "\n", "$$\n", "c = \\frac{b f(a) - a f(b)} {f(a) - f(b)} = b - \\frac{f(b)(a-b)}{f(a) - f(b)}\n", "$$\n", "\n", ":::{figure-md} false-pos-fig\n", "\"false-pos-fig\"\n", "\n", "Method of false position (From Wikimedia)\n", ":::\n", "\n", "### 알고리즘\n", "* 해가 구간 (a, b) 사이에 있을 때 해가 존재하면 $f(a)\\cdot f(b) < 0$ 조건을 활용한다.\n", "\n", "* 이 경우 중간 값 $c=b - \\frac{f(b)(a-b)}{f(a) - f(b)}$ 에 대해 \n", "\n", " * $f(a)\\cdot f(c) < 0$ 이면 해가 (a, c) 사이에 있다고 범위를 좁힘\n", " \n", " * $f(c)\\cdot f(b) < 0$ 이면 해가 (c, b) 사이에 있다고 범위를 좁힘" ] }, { "cell_type": "code", "execution_count": 32, "id": "8e9ad65d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 12 14.930869492487908 14.815076015455954 0.0009442551875167577 0.007815921896799652\n", "1 12 14.815076015455954 14.802632653525668 0.00010354997437138706 0.0008406181671557055\n", "2 12 14.802632653525668 14.80129662906239 1.3284760077999972e-05 9.026401515760205e-05\n", "3 12 14.80129662906239 14.801153195602156 3.5940303191052445e-06 9.690694930243335e-06\n", "4 12 14.801153195602156 14.801137796968773 2.553659442379048e-06 1.040368219980068e-06\n", "Converged at 14.801136143814386\n" ] } ], "source": [ "a, b = 12, 16\n", "c = b - f(b)*(a-b)/(f(a) - f(b))\n", "\n", "c_ex = 14.8011\n", "\n", "# 상대오차 (참, 근사)\n", "eps_t = []\n", "eps_a = []\n", "\n", "iter_max = 20\n", "for i in range(iter_max):\n", " if f(a)*f(c) < 0:\n", " b = c\n", " elif f(b)*f(c) < 0:\n", " a = c\n", "\n", " # Save old midpoint\n", " c0 = c\n", " \n", " # Compute new midpoint\n", " c = b - f(b)*(a-b)/(f(a) - f(b))\n", " \n", " # Compute relative error\n", " eps_ti = abs((c - c_ex)/c_ex)\n", " eps_ai = abs((c0 - c)/c)\n", " eps_t.append(eps_ti)\n", " eps_a.append(eps_ai)\n", " \n", " if eps_ai < 1e-6:\n", " # Stop and write converged solution\n", " print(\"Converged at {}\".format(c))\n", " break\n", " else:\n", " print(i, a, b, c, eps_ti, eps_ai)" ] }, { "cell_type": "code", "execution_count": 33, "id": "94df57e6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Error')" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.semilogy(eps_t)\n", "plt.semilogy(eps_a)\n", "\n", "plt.legend(['True', 'Approximation'])\n", "plt.xlabel('Iter')\n", "plt.ylabel('Error')" ] }, { "cell_type": "markdown", "id": "11fd96cc", "metadata": {}, "source": [ "### DIY\n", "Method of False Position 함수를 `For-loop` 버전과 `Recursive algorithm` 버전으로 완성하시오." ] }, { "cell_type": "markdown", "id": "ca1ecaf1", "metadata": {}, "source": [ "### 문제점\n", "- 곡률이 큰 함수에서 수렴이 매우 느릴 수 있다.\n", "\n", "x 가 $[0, 1.3]$ 사이일 때 아래 함수의 해를 구하시오.\n", "\n", "$$\n", "f(x) = x^{10} - 1\n", "$$" ] }, { "cell_type": "code", "execution_count": 34, "id": "22a9a685", "metadata": {}, "outputs": [], "source": [ "# 함수 정의\n", "f = lambda x : x**10 - 1" ] }, { "cell_type": "code", "execution_count": 35, "id": "53a472c0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 1.3, 131)\n", "\n", "plt.plot(x, f(x))\n", "plt.plot([1], [0], marker='x')\n", "\n", "plt.xlabel('x')\n", "plt.ylabel('y')" ] }, { "cell_type": "code", "execution_count": 36, "id": "7240b968", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 0.65 1.3 0.9750000000000001 0.02499999999999991 0.33333333333333337\n", "1 0.9750000000000001 1.3 1.1375000000000002 0.13750000000000018 0.1428571428571429\n", "2 0.9750000000000001 1.1375000000000002 1.0562500000000001 0.05625000000000013 0.07692307692307696\n", "3 0.9750000000000001 1.0562500000000001 1.015625 0.015625 0.04000000000000013\n", "4 0.9750000000000001 1.015625 0.9953125 0.004687499999999956 0.020408163265306076\n", "5 0.9953125 1.015625 1.00546875 0.005468749999999911 0.01010101010100997\n", "6 0.9953125 1.00546875 1.000390625 0.0003906250000000888 0.005076142131979517\n", "7 0.9953125 1.000390625 0.9978515625000001 0.0021484374999999334 0.002544529262086536\n", "8 0.9978515625000001 1.000390625 0.9991210937500001 0.0008789062499998668 0.0012706480304956191\n", "9 0.9991210937500001 1.000390625 0.9997558593750001 0.00024414062499988898 0.0006349206349206127\n", "10 0.9997558593750001 1.000390625 1.0000732421875 7.324218750004441e-05 0.00031735956839092034\n", "11 0.9997558593750001 1.0000732421875 0.9999145507812501 8.544921874986677e-05 0.00015870496746539284\n", "12 0.9999145507812501 1.0000732421875 0.9999938964843751 6.103515624911182e-06 7.934618741565026e-05\n", "13 0.9999938964843751 1.0000732421875 1.0000335693359377 3.3569335937677636e-05 3.9671519816012954e-05\n", "14 0.9999938964843751 1.0000335693359377 1.0000137329101564 1.3732910156383227e-05 1.9836153373182286e-05\n", "15 0.9999938964843751 1.0000137329101564 1.0000038146972656 3.814697265625e-06 9.918175055922961e-06\n", "16 0.9999938964843751 1.0000038146972656 0.9999988555908204 1.144409179643091e-06 4.9591121205215245e-06\n", "17 0.9999988555908204 1.0000038146972656 1.0000013351440429 1.3351440428799322e-06 2.4795499119667293e-06\n", "18 0.9999988555908204 1.0000013351440429 1.0000000953674317 9.536743172944284e-08 1.2397764929161892e-06\n", "Converged at 0.999999475479126\n" ] } ], "source": [ "a, b = 0, 1.3\n", "c = 0.5*(a+b)\n", "\n", "c_ex = 1\n", "\n", "# 상대오차 (참, 근사)\n", "eps_t = []\n", "eps_a = []\n", "\n", "# 해석 결과\n", "cs = []\n", "\n", "iter_max = 25\n", "for i in range(iter_max):\n", " if f(a)*f(c) < 0:\n", " b = c\n", " elif f(b)*f(c) < 0:\n", " a = c\n", "\n", " # Save old midpoint\n", " c0 = c\n", " \n", " # Compute new midpoint\n", " c = 0.5*(a + b)\n", " cs.append(c)\n", " \n", " # Compute relative error\n", " eps_ti = abs((c - c_ex)/c_ex)\n", " eps_ai = abs((c0 - c)/c)\n", " eps_t.append(eps_ti)\n", " eps_a.append(eps_ai)\n", " \n", " if eps_ai < 1e-6:\n", " # Stop and write converged solution\n", " print(\"Converged at {}\".format(c))\n", " break\n", " else:\n", " print(i, a, b, c, eps_ti, eps_ai)" ] }, { "cell_type": "code", "execution_count": 37, "id": "e3422934", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 1.3, 131)\n", "\n", "plt.plot(x, f(x))\n", "plt.plot(cs, np.zeros_like(cs), marker='x')\n", "\n", "plt.legend([r\"$x^{10} -1$\", 'Bisection method'])\n", "plt.xlabel('x')\n", "plt.ylabel('y')" ] }, { "cell_type": "code", "execution_count": 38, "id": "84e50b43", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Error')" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.semilogy(eps_t)\n", "plt.semilogy(eps_a)\n", "\n", "plt.legend(['True', 'Approximation'])\n", "plt.xlabel('Iter')\n", "plt.ylabel('Error')" ] }, { "cell_type": "code", "execution_count": 39, "id": "3038f3bd", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 0.09429959537232735 1.3 0.1817588725190793 0.8182411274809207 0.48118298674839827\n", "1 0.1817588725190793 1.3 0.2628740125203042 0.7371259874796958 0.3085704030745893\n", "2 0.2628740125203042 1.3 0.3381051033222693 0.6618948966777307 0.22250800139581925\n", "3 0.3381051033222693 1.3 0.4078779165927523 0.5921220834072477 0.17106298338811027\n", "4 0.4078779165927523 1.3 0.4725831535623899 0.5274168464376101 0.13691820472626154\n", "5 0.4725831535623899 1.3 0.5325715106320141 0.46742848936798587 0.11263906512467173\n", "6 0.5325715106320141 1.3 0.5881445691706797 0.4118554308293203 0.09448877274685547\n", "7 0.5881445691706797 1.3 0.6395439707682155 0.36045602923178455 0.08036883145938375\n", "8 0.6395439707682155 1.3 0.6869431667412387 0.3130568332587613 0.06900017100086796\n", "9 0.6869431667412387 1.3 0.7304464366929376 0.26955356330706237 0.05955709791488338\n", "10 0.7304464366929376 1.3 0.7700987444968072 0.22990125550319285 0.05148990059681097\n", "11 0.7700987444968072 1.3 0.8059075090169237 0.19409249098307635 0.044432846349573514\n", "12 0.8059075090169237 1.3 0.8378738914244523 0.16212610857554766 0.03815178242776284\n", "13 0.8378738914244523 1.3 0.8660276320873558 0.13397236791264422 0.03250905585430972\n", "14 0.8660276320873558 1.3 0.8904572813509997 0.10954271864900034 0.02743494806014644\n", "15 0.8904572813509997 1.3 0.9113282513082279 0.08867174869177208 0.022901704108555406\n", "16 0.9113282513082279 1.3 0.9288846695992142 0.07111533040078577 0.01890053616512088\n", "17 0.9288846695992142 1.3 0.9434360517492835 0.056563948250716534 0.015423813965015026\n", "18 0.9434360517492835 1.3 0.955333975192147 0.04466602480785298 0.012454203191580743\n", "19 0.955333975192147 1.3 0.9649455723416893 0.03505442765831068 0.009960766104369261\n", "20 0.9649455723416893 1.3 0.9726296888054463 0.027370311194553687 0.007900351544064411\n", "21 0.9726296888054463 1.3 0.9787191336334623 0.0212808663665377 0.00622185121221563\n", "22 0.9787191336334623 1.3 0.9835099523268419 0.016490047673158093 0.004871144091674134\n", "23 0.9835099523268419 1.3 0.9872569173655359 0.012743082634464109 0.0037953292327316803\n", "24 0.9872569173655359 1.3 0.9901736307394302 0.00982636926056979 0.0029456585020510096\n" ] } ], "source": [ "a, b = 0, 1.3\n", "c = b - f(b)*(a-b)/(f(a) - f(b))\n", "\n", "c_ex = 1\n", "\n", "# 상대오차 (참, 근사)\n", "eps_t = []\n", "eps_a = []\n", "\n", "# 해석 결과\n", "cs = []\n", "\n", "iter_max = 25\n", "for i in range(iter_max):\n", " if f(a)*f(c) < 0:\n", " b = c\n", " elif f(b)*f(c) < 0:\n", " a = c\n", "\n", " # Save old midpoint\n", " c0 = c\n", " \n", " # Compute new midpoint\n", " c = b - f(b)*(a-b)/(f(a) - f(b))\n", " cs.append(c)\n", " \n", " # Compute relative error\n", " eps_ti = abs((c - c_ex)/c_ex)\n", " eps_ai = abs((c0 - c)/c)\n", " eps_t.append(eps_ti)\n", " eps_a.append(eps_ai)\n", " \n", " if eps_ai < 1e-6:\n", " # Stop and write converged solution\n", " print(\"Converged at {}\".format(c))\n", " break\n", " else:\n", " print(i, a, b, c, eps_ti, eps_ai)" ] }, { "cell_type": "code", "execution_count": 40, "id": "4a3d23ea", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 1.3, 131)\n", "\n", "plt.plot(x, f(x))\n", "plt.plot(cs, np.zeros_like(cs), marker='x')\n", "\n", "plt.legend([r\"$x^{10} -1$\", 'Method of False Position'])\n", "plt.xlabel('x')\n", "plt.ylabel('y')" ] }, { "cell_type": "code", "execution_count": 41, "id": "bab4a0f9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Error')" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.semilogy(eps_t)\n", "plt.semilogy(eps_a)\n", "\n", "plt.legend(['True', 'Approximation'])\n", "plt.xlabel('Iter')\n", "plt.ylabel('Error')" ] }, { "cell_type": "markdown", "id": "11779255", "metadata": {}, "source": [ "## SciPy 활용\n", "`scipy.optimize` 모듈은 최소화, Curve fitting 그리고 root finding과 관련된 다양한 알고리듬을 제공한다.\n", "\n", "**참고**\n", "* https://scipy-lectures.org/intro/scipy.html#optimization-and-fit-scipy-optimize\n", "* https://docs.scipy.org/doc/scipy/reference/optimize.html" ] }, { "cell_type": "code", "execution_count": 42, "id": "ec4f3ef8", "metadata": {}, "outputs": [], "source": [ "from scipy.optimize import root_scalar\n", "# root_scalar?" ] }, { "cell_type": "code", "execution_count": 43, "id": "f866698c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ " converged: True\n", " flag: converged\n", " function_calls: 10\n", " iterations: 9\n", " root: 0.9999999999998475\n", " method: brentq" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "root_scalar(f, bracket=[0, 1.3])" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.5" } }, "nbformat": 4, "nbformat_minor": 5 }